How can I explain to a non-Muslim, that marriage between a Muslim and a non-Muslim is not permitted?

Praise be to Allah, the Lord of the Worlds; and may His blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.

It is not permissible for a Muslim woman to marry a non Muslim man at all as Allah says: "And give not (your daughters) in marriage to Al-Mushrikûn till they believe (in Allah Alone)." (Al-Baqarah 2:221)

Al-Qurtubi said: "The above verse means that we must not marry a Muslim woman to a Kafir (a non-Muslim). The Ummah (Muslim nation) agreed in a consensus that a non-Muslim should not marry a Muslim woman under any circumstances, because allowing so is an offence to Islam".

So the above statement clarifies the wisdom why it is not permissible for a Muslim woman to marry a non-Muslim man.

Doctor Al-Qardawi, in his book Al-Halal Wal Haram says: "The basis for this is that the husband must respect the belief of his wife in order to preserve the good martial relationship between them. The woman of the People of the Book lives under the guardianship of her husband who respects the origin of her religion, book and Prophet, and even says, that he will not be a true believer except if he believes in that. Whereas a Jew, or a Christian does not believe in the slightest thing in Islam, or in the book of Islam, or in the Prophet of Islam. Therefore, how could it be possible for a Muslim woman to live with him while her religion requires of her to perform some ritual acts of worship and obligations, legislates things for her and forbids her to do other things? It will also be impossible for the Muslim woman to respect her religion while her husband completely denies and rejects her faith. Hence, Islam is logical when it forbids a Muslim woman to marry an idolater because Islam completely rejects Shirk (associating partners with Allah) and idol worship, so how can affection, kindness and mercy exist between the two".

Allah knows best.